Of course much will depend on what camera mount you are using, as not every brand offers the same lenses - and different people have different needs as far as what to improve upon from a 'standard' kit lens in the typical 18-50mm range and usually a slowish F3.5-5.6 or so.
Some find upgrading the aperture and staying within the same focal range to be useful - something like a 16-50mm F2.8. Others find getting a little more reach to be more useful overall, going to something like an 18-135mm extended kit. Still others want an all-in-one lens solution that can allow them to never really have to change lenses - something like an 18-250mm or 18-400mm.
Personally, I find an 18-135mm to be a great 'kit' lens - more reach than a typical kit, still compact and easy to carry, and for general purpose shooting it can cover about 90% of needs with still good optical quality throughout the range.
Despite having a collection of 30+ lenses and 3 camera bodies, my last two trips to Disney in July and September this year, in the hot and humid conditions where I didn't want to deal with a bag-o-lenses, I ended up shooting with just two lenses: 18-135mm F3.5-5.6, and 16mm F1.4 prime for dark ride/low light.